A mechanical resonator using a microfabrication technique has received attention in recent years.
One example of a conventional mechanical resonator will be described with reference to FIG. 33. FIG. 33 is a simplified diagram showing a configuration of a mechanical vibration filter using flexural vibration proposed in Non-patent Reference 1.
This filter is formed by patterning on a silicon substrate using a thin film process, and is constructed of an input rail 104, an output rail 105, straddle mounted beams 101, 102 placed at an air gap of 1 μm or less with respect to the respective rails, and a coupling beam 103 for coupling the two beams. A signal inputted from the input rail 104 is capacitively coupled to the beam 101 and generates electrostatic force in the beam 101. A filtering output of the input signal is constructed so as to be fetched by exciting mechanical vibration only when a frequency of the signal matches with the vicinity of a resonance frequency of an elastic structural body made of the beams 101, 102 and the coupling beam 103 and further detecting this mechanical vibration as a change in capacitance between the output rail 105 and the beam 102.
In the case of being set at an elastic modulus E, a density ρ, a thickness h and a length L for a straddle mounted beam with a rectangular cross section, a resonance frequency f of flexural vibration is shown by the following formula.
                    f        =                  1.03          ⁢                      h                          L              2                                ⁢                                    E              ρ                                                          [                  Mathematical          ⁢                                          ⁢          formula          ⁢                                          ⁢          1                ]            
When a material is set at polysilicon, it becomes E=160 GPa and ρ=2.2×103 kg/m3 and also when dimensions are set at L=40 μm and h=1.5 μm, it becomes f=8.2 MHz and a filter with a band of about 8 MHz can be constructed. Steep frequency selection characteristics with a high Q value can be obtained by using mechanical resonance as compared with a filter constructed of a passive circuit such as a capacitor or a coil.
However, in the construction described above, there are the following restrictions in the case of constructing a filter having a higher frequency band. That is, it is apparent from (mathematical formula 1) that it is first desirable to change a material and increase E/ρ, and when E is increased, the amount of displacement becomes small even when force of flexing a beam is equal, and it becomes difficult to detect displacement of the beam.
Also, when an index representing flexibility in a beam is set at a ratio d/L between a length L of the beam and the amount d of flexure of the beam center at the time of applying a static load to a beam surface of a straddle mounted beam, d/L is expressed by a proportional relation of the following formula.
                              d          L                ∝                                            L              3                                      h              3                                ·                      1            E                                              [                  Mathematical          ⁢                                          ⁢          formula          ⁢                                          ⁢          2                ]            
From these, in order to increase a resonance frequency while holding a value of d/L, at least E cannot be changed and it is necessary to obtain a material with a low density ρ, and it is necessary to use a composite material such as CFRP (Carbon Fiber Reinforced Plastics) as the material with a low density at a Young's modulus equal to that of polysilicon. In this case, it becomes difficult to construct a micromechanical vibration filter in a semiconductor process.
Hence, a second method without using such a composite material includes a method for increasing h·L−2 by changing a dimension of a beam in (mathematical formula 1). However, an increase in the thickness h of the beam and a decrease in the length L of the beam result in a decrease in d/L of (mathematical formula 2) which is an index of flexibility and it becomes difficult to detect flexure of the beam.
When a relation between log(L) and log(h) is shown in FIG. 34 with respect to (mathematical formula 1) and (mathematical formula 2), a straight line a has a relation obtained from (mathematical formula 1) and a straight line b has a relation obtained from (mathematical formula 2). In this FIG. 34, in the case of selecting h and L in the range (region A) upper than a straight line with a gradient “2” using a point A of the present dimension as an initial point, f becomes large and in the case of selecting h and L in the range (region B) lower than a straight line with a gradient “1”, d/L becomes large. Therefore, the hatch portion (region C) in FIG. 34 is in the range of h and L capable of increasing a resonance frequency while ensuring the amount of flexure of the beam.
It is apparent from FIG. 34 that miniaturization of both dimensions of the length L of the beam and the thickness h of the beam is a necessary condition in a higher frequency of a mechanical vibration filter and miniaturization of L and h at the same scaling, that is, a decrease in L and h while being placed on the straight line with the gradient of 1 is a sufficient condition of the hatch portion of FIG. 34.
By miniaturizing a dimension of a mechanical vibrator in a conventional mechanical resonator thus, a resonance frequency can be increased. However, there was a problem that the case where a mechanical Q value reduces and the Q value necessary to obtain desired frequency selection characteristics cannot be obtained occurs by miniaturizing the dimension generally.
Hence, a resonator using a single-crystal material is contemplated as a resonator with a good Q value. In a vibrator of the single-crystal material, internal atoms are regularly arranged, so that a higher Q value can be obtained as compared with a polycrystalline material. For example, FIG. 35 is a straddle mounted beam structure fabricated by processing an SOI layer of a silicon substrate 204 constructing an SOI (Silicon on Insulator) substrate shown in Non-patent Reference 2. However, in this structure, a beam can be vibrated by removing a BOX (Buried Oxide) layer 203 under the SOI layer using hydrofluoric acid and the BOX layer under a support part 205 is also removed and the support part becomes brittle. Consequently, vibration of the support part 205 becomes nonnegligible and with a decrease in a resonance frequency of a straddle mounted beam, dissipation of vibration energy from the support part occurs, so that it becomes difficult to obtain a large Q value.
Hence, an example of improving brittleness of the support part 205 by thickening a thickness of the support part 205 more sufficiently than a thickness of a vibrator 201 constructing a beam is disclosed in Non-patent Reference 3. FIG. 36 is a structure of the vicinity of a support part 205 of a straddle mounted beam shown in Non-patent Reference 3. A thickness of the support part 205 is a thickness of a silicon substrate 204 and a thickness of the beam is thin sufficiently with respect to the thickness of the silicon substrate and therefore, the support part 205 has a robust structure. However, a structure of the support part is not axisymmetrical with respect to a length direction of the beam, so that the support part 205 becomes brittle as the support part of one side (for example, the side A) with respect to the axis retracts in the length direction of the beam. Since the side A and the side A′ of the support part 205 are formed by dry etching and individual lithography of two times, high-accuracy alignment of the lithography of two times is required in order to reduce retraction of one side. It becomes very difficult to perform this alignment step as a dimension of the vibrator becomes fine from the order of μm to the order of nm.
Also, in the method of fabrication of the vibrator of Non-patent Reference 3, it is difficult to approach the vibrator 201 and form an electrode 202. FIG. 37 is a diagram showing cross sections of the substrate and the vibrator of FIG. 36. Since there is an opening part between the substrate and the vibrator as shown in FIG. 37A, in the case of attempting to form the electrode 202 proximate to a side surface of the vibrator 201 by a thin-film formation technique such as sputtering, there is the opening part, so that the electrode cannot be anchored to the substrate or a robust electrode structure cannot be formed because a thickness of the electrode near to the opening part becomes extremely thin as shown in FIG. 37B.
There is also a technique in which boron is diffused from a surface of a silicon substrate and anisotropic etching is performed from a back surface of the silicon substrate and a diffusion layer of the boron is used as an etching stop layer of the anisotropic etching (Non-patent Reference 4). When a diffusion region of boron is formed in a beam shape, a beam type vibrator can also be formed as shown in FIG. 38. An electrode can be formed on the substrate surface since there is no opening part on the substrate surface before the anisotropic etching is performed. However, an effect of an etching stop varies depending on variations in diffusion of boron, so that it was difficult to obtain a beam shape having a predetermined dimension and it was extremely difficult to obtain a desired value with respect to a resonance frequency. Also, a surface of the vibrator is not flat, so that loss of vibration energy resulting from surface roughness occurs and a Q value reduces.
Also, a smaller vibrator must be formed in order to increase a resonance frequency of a resonator to a VHF band or a UHF band. With this, an opposite area of the vibrator and the electrode becomes smaller, so that capacitance becomes small and also an impedance becomes high. In a high-frequency signal, energy loss of an RF signal increases when the extent of an impedance mismatch becomes high. As this solution method, there is a method for reducing an impedance by electrically connecting plural resonators in parallel and approaching a match state. FIG. 39A is a resonator constructed of a vibrator using aluminum as a material. A vibrator 201 has a straddle mounted beam structure and is supported by a support part 205. An electrode 202a for excitation and an electrode 202b for detection are placed on both side surfaces of the vibrator 201 through gaps. In this configuration, the vibrator 201 produces flexural vibration in a direction attracted in a direction of the electrode 202a for excitation and its resonance frequency is 35.5 MHz. FIG. 39B is a configuration of electrically connecting plural resonators of FIG. 39A in parallel and reducing an impedance.
FIG. 40A shows impedances at the time of setting the number N of resonators electrically connected in parallel at 1, 10 and 100. However, the individual resonators are fabricated with extremely high dimension accuracy, so that variations in a resonance frequency become substantially 0. As shown in FIG. 40A, the impedance can be reduced without changing resonance characteristics as the number N is increased.
FIG. 40B shows impedances in the case of having variations (0.3 MHz in a standard deviation) in resonance frequencies of individual resonators. In the case of having the variations, as the number N of resonators is increased to 10 and 100, the peak at the resonance frequency is not sharp and it becomes difficult to construct a good resonator.
The variations in resonance frequencies must be suppressed by processing individual resonators with high accuracy in order to electrically connect plural resonators in parallel for reduction in the impedance thus. In a resonance frequency of a straddle mounted beam, a thickness and a length of the beam become predominant in flexural vibration and a length of the beam becomes predominant in torsional vibration, so that it becomes important to manage the thickness and the length of the beam in the case of using flexural resonance and it becomes important to manage the length of the beam in the case of using torsional resonance.                Non-patent Reference 1: Frank D. Bannon III, John R. Clark, and Clark T.-C. Nguyen, “High-QHF Microelectromechanical Filters”, IEEE Journal of Solid-State Circuits, Vol. 35, No. 4, pp. 512-526, April 2000        Non-patent Reference 2: Vincent Agache et. al, “CHARACTERIZATION OF VERTICAL VIBRATION OF ELECTROSTATICALLY ACTUATED RESONATORS USING ATOMIC FORCE MICROSCOPE IN NONCONTACT MODE”, Proc. of IEEE TRANSDUCERS '05, pp. 2023-2026        Non-patent Reference 3: A. Tixier-Mita and others, “SINGLE CRYSTAL NANO-RESONATORS AT 100 MHz FABRICATED BY A SIMPLE BATCH PROCESS”, Proc. of IEEE TRANSDUCERS '05, pp. 1388-1391        Non-patent Reference 4: Chang-Jin Kim and others, “Silicon-Processed Overhanging Microgripper”, Journal of Microelectromechanical Systems, Vol. 1, No. 1, 1992, pp. 31-36        